We have extended our method of grouping Feynman diagrams (GFD theory) to study the transverse and longitudinal correlation functions G⊥(k) and G∥(k) in φ4 model below the critical point (T < T c) in the presence of an infinitesimal external field. Our method allows a qualitative analysis without cutting the perturbation series. The long-wave limit k → 0 has been studied at T < Tc, showing that G⊥(k) ≃ak-λ⊥ and G∥ (k) ≃ bk -λ∥ with exponents d/2 < λ⊥. < 2 and λ⊥= 2λ⊥- d are the physical solutions of our equations at the spatial dimensionality 2 < d < 4, which coincides with the asymptotic solution at T → Tc as well as with a nonperturbative renormalization group (RG) analysis provided in our paper. This has been confirmed also by recent Monte Carlo simulations. The exponents as well as the ratio bM2 /a2 (where M is magnetization) are universal. The results of the perturbative RG method are reproduced by formally setting λ⊥. = 2, although our analysis yields λ⊥ < 2.
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Grickus A.,Liepaja University Engineering for Rural Development | Year: 2015

In circumstances, when it is important to replace insulation materials with high content of emissions during production, it is necessary to create a new heat and sound insulation material, which eliminates CO2 emissions, develop its production techniques and technological machinery - raw material chopper, pulp mixer, termopress, dryer chamber, formatting knives, determine technical control parameters and control equipment, develop a mathematical model of the material and calculation methods for design works. It is necessary to design, manufacture and experimentally test the respective technological equipment for insulation production pilot plant. To get exact physical parameters it is necessary to design, manufacture and test unique laboratory equipment for determining the properties of the insulation material.
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